Welcome to CFC, SKS!
I played many archer rushes at demigod level and a couple at deity. Here is what those games teached me:
. The question you should ask yourself before starting an archer rush is "Do I have enough space to expand peacefully? If the answer is "no!", archer rush is probably a good idea, even if your civ is not designed for early wars. In one of my last DG games, I succesfully played an archer rush with England
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. At demigod level, a good build order is: 2-3 cavemen for scouting, rax, 4-5 archers (or better if you are scientific: 1 spear and 4 archers) and attack while building a setller.
. The ennemy cities are to be captured, not (auto)razed. You need them to compensate the fact you are not REXing.
. After you capture a city, hit the F4 key: the ennemy civ may well offer you free techs or free cities for peace.
. When you are planning to trade peace for techs or cities, kill as many ennemies units you can but let a single one live in your territory (or in what is about to become your territory thanks to the trade). After the peace is signed, send each turn the message "get that f!*#king unit out of my territory or declare war!". The AI is stupid enough to throw away the peace treaty it just bought
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. If you are scientific, start reasearching IW the very turn you decided to follow the archer rush strategy. Swords are perfect continuation for archer rushes.
. The F7 key is your friend: it lets you know which city you dont want to capture immediately. (The AI never cancels the build of a GW).
. Demigod is the level where archer rushes are the most profitable: the AI starts with 2 settlers and a weak military. IOW it will have 4 poorly defended, cities when you get your archer stack.